Sundials have been in use since ancient times and usually involve some means of casting a shadow onto an analog scale containing time markers. Similar to the hour hand of a regular clock, the position of the shadow on this scale indicates the current time. While many different variations of this basic principle have been proposed, few deal with the disadvantages of an analog displays which requires a certain skill of the observer and is limited in accuracy. Using a digital display overcomes these disadvantages, as evidenced by the success of digital clocks and watches. The object of the present invention is to transfer this advance to the domain of sundials.
A fictitious digital sundial was described in Ian Stewart's column "Mathematical Recreations" (Ian Stewart, "What in heaven is a digital sundial?", Scientific American, pages 104-106, 1991). In his article, Stewart builds on an idea first presented in Kenneth Falconer's book "Fractal Geometry" on page 89 (Kenneth Falconer, Fractal Geometry--Mathematical Foundations, John Wiley and Sons, 1990): In order to illustrate a theorem on the projection of fractals, Falconer describes a hypothetical digital sundial based on a three-dimensional fractal that casts different shadows in the shape of numbers.
This device, although mathematically plausible, can not be realized in practice for several reasons. Fractals have infinitesimally small structure, which would impede manufacturing of the device; furthermore, the theorem does not yield a method of constructing such a fractal. Most importantly, the theorem relies on a point-shaped light source and on geometrical optics (including straight-line projection), neither of which is true in the physical world, since (a) the disk of the sun subtends an angle of about one-half degree, and (b) diffraction of light imposes a lower limit on the size of any optical structure, so that a fractal with its infinitesimally small detail can not be used. Thus, even if it were be possible to manufacture such a fractal device, the laws of physics would prevent it from working.
A holographic sundial has been proposed which overcomes some of these problems by exploiting the wave nature of light (A. Gongora-T. and R. Stuart, "Holographic sundial", Applied Optics, 29:32, pages 4751-4752, 1990). The main disadvantage of this approach is the long and costly manufacturing process of the device, in which each displayed image has to be recorded separately, and the photographic material needs to be reoriented for each exposure. Furthermore, shrinkage of the photographic emulsion limits the angular precision.
Hungarian patent T62415 to Haszpra (1990) (international patent WO 94/03844) discloses a sundial with a transparent time scale whose shadow onto a viewing surface containing an index line indicates the time. Although the title of the patent claims a digital sundial, the device is just a variation of the traditional analog sundial, reversing the roles of shadow casting gnomon and time scale. Similar such variations include U.S. Pat. No. 2,931,102 to Thew (1960), and also U.S. Pat. No. 4,255,864 to Glendinning (1981) and U.S. Pat. No. 5,056,232 to Cunningham (1991), in which the sunlight itself marks the time on an analog scale in form of a bright projected line.
U.S. Pat. No. 4,782,472 to Hines (1988) discloses a solar clock with a digital display, in which a light gathering tube casts the sunlight onto an array of optical fibers that are coupled to a seven-segment display. This invention actually comprises a physically realizable digital sundial, but it has the drawback that the device is quite complex, and thus expensive to manufacture. Furthermore, since the light gathering tube and the display are two separate units only connected by a cable of optical fibers, it is not immediately obvious to the observer that the sun is responsible for creating the image of the time on the display (as opposed to, say, an electronic circuit). Having many components makes the device difficult to install and prone to damage. Finally, the principle underlying the invention only allows displays with a small number of discrete elements (such as seven-segment displays), and increasing the number of elements also increases the complexity of the device.
In light of the above, objects and advantages of the present invention are to provide a digital sundial which is physically realizable, which can be manufactured easily and inexpensively, which consists only of a few components and thus is robust, which is unlimited in the contents to be displayed, and whose function as a digital sundial is immediately apparent to an observer.
A more general object of the present invention is to provide an optical apparatus for digitally displaying the angular direction of a remote light source.